Is music/sound similarity comparison feasible on neural networks?
Yes, it is possible, even if the best approach could be different from  neural networks. Anyway, you should extract some significant features from the audio (energy, onsets, root frequencies, and other). Usually, more features than those really needed are extracted and afterwards the most sigificant are selected through some algorithm (e.g. PCA). In this way you will obtain an array of features (say between 10 and 100 features) with which you can train your NNs.

Note that NNs do not tell you why two audio are similar but only if they are or not. This is a big disadvantage. Instead, algorithms based on grey-box modeling such as rule or case based algorithm (maybe using fuzzy logic) could be more useful, provided that you have a deeper knowledge of the problem.

References and deepening sources: SMC Lab from University of Padua education material